SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVAL(Ⅱ)

In this paper the existence of solutions of the singularly perturbed boundary value problems on infinite interval for the second order nonlinear equation containing a small parameteris examined, where are constants, and i=0,1 . Moreover, asymptotic estimates of the solutions for the above problems are given.

ON PL TYPE WEIGHTED LACUNARY (0,2;0)-INTERPOLATION ON INFINITE INTERVAL (-∞,+∞)

In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS ON INFINITE INTERVAL(Ⅰ)

In this paper existence, uniqueness and asymptotic estimations of solutions of the boundary value problems on infinite interval for the second order nonlinear equation depending singularly on a small parameterare examined, where are constants, and i=0,1.

ORTHOGONAL POLYNOMIALS ON INFINITE INTERVALS AND PROBLEM 54 OF P.TURAN

In this paper some new results for general orthogonal polynomials on infinite intervals are presented. In particular, an answer to Problem 54 of P. Turan[J. Approximation Theory, 29(1980),P.64] is given.

An Upper and Lower Solution Theory for the Problem(G′(y))′+f(t,y)=0 on Finite and Infinite Intervals

A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.

EXISTENCE OF UNBOUNDED SOLUTIONS FOR A n-TH ORDER BVPS WITH A p-LAPLACIAN

This paper considers the solvability of boundary value problems with a p-Laplacian {(φ(u^((n-1))(t)))'=q(t)f(t,u(t),…,u^((n-1))(t)),0<t<+∞,u^((i))(0)=Ai,i=0,1,…,n-3,u^((n-2))(0)-au^((n-1))(0)=B,u^((n-1))(+∞)=C.By using the methods of upper and lower solution, the schauder fixed point theorem, and the degree theory, we obtain the existence of one and triple solutions. This paper generalizes several problems due to the dependence on the p-Laplacian operator, the n-1-th derivative not only in the differential equation but also in the boundary conditions. The most interesting point is that the solutions may be unbounded.

CALCULUS OF VARIATIONS WITH DIRICHLET BOUNDARY VALUE PROBLEM FOR PERTURBED SECOND-ORDER DIFFERENTIAL EQUATIONS ON A HALF-LINE

Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.